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Answer:
Must add: 202
Step-by-step explanation:
[tex]The \ formula \ for \ perfect \ square => (a + b)^2 = a^2 + 2ab + b^2[/tex]
a = x
2ab = 26x
2ab = 26a [ substitute a instead of x]
[tex]b = \frac{26a}{2a}[/tex]
b= 13
So,
[tex](x + 13)^2 = x^2 + 26x + 169[/tex]
But given equation is :
[tex]x^2 + 26x = 33\ => \ x^2 + 26x -33 = 0[/tex]
We have find the difference between 169 and -33 to get the number that should be added to get the perfect square.
That is , 169 - (-33) = 202
Therefore ,
[tex]x^2 + 26x -33 + 202 \ makes \ given \ equation \ a \ perfect \ square[/tex]
Multiply by 4a
21²=441 must be added to get complete square
Remark
You can also add 13² =169 as 2(13)(x)=26x